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Frölicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds
Hisashi Kasuya, Jonas Stelzig
For complex parallelisable manifolds , with a solvable or semisimple complex Lie group, the Frölicher spectral sequence degenerates at the second page. In the so…
Remarks on Dolbeault cohomology of Oeljeklaus-Toma manifolds and Hodge theory
Hisashi Kasuya
We give explicit harmonic representatives of Dolbeault cohomology of Oeljeklaus-Toma manifolds and show that they are geometrically Dolbeault formal. We also give explicit harmonic…
Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds
Hisashi Kasuya
For a -dimensional compact Sasakian manifold, if , we prove that the analytic germ of the variety of representations of the fundamental group at every semi-simple rep…
Non-invariant deformations of left-invariant complex structures on compact Lie groups
Hiroaki Ishida, Hisashi Kasuya
We consider deformations of left-invariant complex structures on simply connected semisimple compact Lie groups which are a priori non-invariant. Computing their cohomologies, we s…